When a lawyer represents a client charged with a criminal offense, the normal course of action is to meet with the client and listen to their side of the story. The lawyer will question the client about inconsistencies, reported facts that can not be established, State evidence that does not cooroborate the client's story, etc. as the representation continues its course through the discovery stages etc.
KC going to Baez's office everyday was a bit extraordinary, but remember he didn't want her to be coerced into saying something to her own detriment to her family or the BH's. I would have done the same thing. I am sure that they had long, long talks about the law, the charges, the evidence, and the lack of any coorboration of KC's stories, characters, places, etc.
If you aren't an attorney, then it is hard for you to imagine how intimate the relationship is with the client and no, it is not sexual at all. We become emersed in our client's well being and get to know them very well, their families and remain connected to them for life. When the case is over it is very tough for the client because they become very dependant on their lawyer. It is hard when they have to realize that the attorney is now completely emersed in another client.
I hug my clients, I hold their hands through depositions and trials, they cry on my shoulder, they find comfort in my office where they are not judged by anyone and it is the one place where everyone is happy to see them.
If a client confesses to his or her attorney that he/she committed the crime for which they are charged, the lawyer can continue to represent the client. The thing that the lawyer can not do is to offer false evidence of innocence (false alibis) or to subjorn perjury from a witness, i.e., the lawyer can not put the client on the stand and ask the client "did you kill XYZ" knowing that the client will lie and say "No."
If the client has confessed to the lawyer, he/she must still provide a vigorous defense. This could mean challenging the evidence collection, testing, the LE testimony,etc. Even a guilty client is entitled to have the State prove their guilt beyond a reasonable doubt and the lawyer's job is to make sure the State sustains it's burden of proof. When faced with overwhelming evidence, the lawyer is required to offer his/her best advice based on all the circumstances of the case and this is where they begin to talk about plea bargains, etc. However, if the client refuses to make any deal, the lawyer can continue to represent the client through trial, with the limitations expressed above.
The problem is that it is hard to represent someone adequately if you are already of the mind-set that they are guilty liars. This is where you are exposed to "surprises" as the client continues to get caught lying with proof of the lies presented by the State. There must be mutual trust between the client and the attorney or things are not going to work at all.
Baez can terminate his representation any time he wishes, however it is very prejudicial to the client to do so at the last minute before trial and is frowned upon by the court and the Bar.
I see all the criticism of Baez, but I can't see where he has done anything unethical or prejudicial to KC's interests. From what I see, he is a competent attorney and KC trusts him so that is all that matters. Is there any question but that he is on her side, her defender? No. I think she is in good hands and he is doing a great job.